Does the Quran permit sexual relations outside of marriage?

Recently, we have been engaged in some online debates with Muslims, specifically Osama
Abdallah, regarding the Quran permitting a form of prostitution called Muta. Refer to these
articles (*, *, *)
for details.

Osama had challenged us to show from the Holy Bible where divorced women were
prohibited from having sexual relations outside the confines of marriage. That challenge
was fully addressed in the above linked articles so we encourage the readers to go there
and read the evidence for themselves.

Osama, in an audio file response to an Arabic Christian debater Christian Prince
(*), also claimed that the Quran forbids
female Muslim slave owners from sleeping with their male slaves:

Also Allah almighty allowed only sex to be done with the female right hand possessions
from out of all of the right hand possessions which include male, males, females, and
animals; and other objects like furniture, for instance, or weapons, or, or objects that
could be used, for instance, for sex, you know I dont want to get graphic but you
get the picture, where small objects could be used for sexual pleasures. These are all,
ah, right hand possessions. But God almighty in the noble Quran made it clear that out
of the right hand possessions, only females are allowed to be, to have, for the Muslims
to have sex with them. And only the male Muslims, not the female, ohm, Muslim masters.
And not, and certainly the female Muslim masters are not allowed to have sex with the,
with the male slaves.
(Audio source)

What makes this truly interesting is that many Muslims cite S. 23:5-6 to prove
that women must remain chaste and need to be married before they can engage in sexual
intimacy, but fail to adequately address what these verses actually say. If one were to
read the context of these citations one would immediately realize that these citations are
expressly permitting both Muslim men and women to have sex as much as they want without
requiring them to first get married:

Successful indeed are the believers, Who are humble in their prayers, And who keep
aloof from what is vain, And who are givers of poor-rate, And who guard their private
parts, Except before their mates (azwajihim) or those whom their right hands
possess, for they surely are not blameable, But whoever seeks to go beyond that,
these are they that exceed the limits; S. 23:1-7 Shakir

The reference to "their mates" includes both the males and the females,
i.e. to the husbands and wives of the believers. The word zawaj can refer to
either spouse and it is not gender specific. Notice how the late A. Yusuf Ali translated
this word:

Except with those joined to them in the marriage bond, or (the captives)
whom their right hands possess, - for (in their case) they are free from blame, S. 23:6

The late Muslim scholar Muhammad Asad wrote in reference to S. 23:6:

Lit., "or those whom their right hands possess" (aw ma malakat aymanuhum).
Many of the commentators assume unquestioningly that this relates to female slaves,
and that the particle aw ("or") denotes a permissible alternative. This
interpretation is, in my opinion, inadmissible inasmuch as it is based on the assumption
that sexual intercourse with ones female slave is permitted without marriage: an
assumption, which is contradicted by the Quran itself (see 4: 3, 24, 25 and 24: 32,
with the corresponding notes). Nor is this the only objection to the above-mentioned
interpretation. Since the Quran applies the term believers" to men and
women alike, and since the term azwaj ("spouses"), too, denotes both the male
and the female partners in marriage, there is no reason for attributing to the phrase ma
malakat aymanuhum the meaning of "their female slaves"; and since, on
the other hand, it is out of the question that female and male slaves could have been
referred to here it is obvious that this phrase does not relate to slaves at all, but has
the same meaning as in 4: 24 - namely, "those whom they rightfully possess through
wedlock (see note on 4: 24) - with the significant difference that in the present context
this expression relates to both husbands and wives, who "rightfully possess" one
another by virtue of marriage. On the basis of this interpretation, the particle aw which
precedes this clause does not denote an alternative ("or") but is, rather, in
the nature of an explanatory amplification, more or less analogous to the phrase "in
other words" or "that is", thus giving to the whole sentence the meaning,
"save with their spouses - that is, those whom they rightfully possess [through
wedlock]", etc. (Cf. a similar construction 25: 62 - "for him who has the
will to take thought -that is [lit., "or"], has the will to be grateful".)
(Asad, fn. 3; source;
bold emphasis ours)

Asad acknowledges that the term azwaj or zawaj are inclusive
terms which refer to either spouse, not just to the wives of the men.

Another Muslim source agrees with Asad:

Commentary: "Azwaj" is the plural of "Zauj"
that is a pair. This is the reason that in Arabic it applies to both,
masculine as well as feminine. Man is the Zauj of woman and woman is
the Zauj of a man... (Riyad-us-Saliheen, compiled by Al-Imam
Abu Zakariya Yahya bin Sharaf An-Nawawi Ad-Dimashqi, commentary by Hafiz
Salahuddin Yusuf, revised by M.R. Murad [Darussalam Publishers &
Distributors, Riyadh, Houston, New York, Lahore, First Edition: June 1999],
Volume 2, Book Fourteen - The Book of Supplicating Allah to Exalt the Mention
of Allah's Messenger (phuh), Chapter 243: The Obligation of Supplicating Allah
to Exalt His Mention and its Excellence, and its Manner, Number 1407, p. 1042,
source)

What this basically means is that this text is explicitly allowing even women to have
sexual relations with slaves that they own. Thus, we have a clear statement from Allah
permitting women to engage in sexual relations outside the confines of marriage.

This isnt merely our understanding of the reference, since one Muslim narration
even admits that this is how certain Muslims understood it:

Qatadah said, "A woman slept with her male slave so they brought her to Umar.
And they told him she understood verse 23:6 to say that, so Umar shaved
the male slave head and let her go after expelling the slave from Madina and said
the woman shouldnt marry any one after that." (Tafsir Ibn Kathir on Sura 23:6;
online
source; bold and underline emphasis ours)

Notice the passage that was cited to justify what the woman had done with her male
slave. They clearly understood Sura 23:6 to be permitting even the women to enjoy sexual
intimacy with their slaves without being required to marry them. Now how did Umar respond?
Did he use a Quranic verse to refute them or did he simply forbid them from engaging in
sexual relations even though they cited a Quranic text to support their case? Which holds
more authority, the Quran or Umars arbitrary interpretations and decrees?

As it stands, this passage is formulated gender neutral, i.e. it applies to both male
and female believers, and thus indeed permits Muslim men and Muslim women to have
sex with those whom their right hands possess without needing to be married first.

The Bible is clear. Sexual relations are only allowed within marriage. For Islam
there remains a final question: Why would sexual intercourse with a male slave be
a sin for a woman although it is taken for granted that Muslim men have the right
to have sexual relations with their slave women without having to marry them?

Following Umar, many Muslims today may want to restrict the permission for
immorality to Muslim men, but the Quran allows sexual relations outside of marriage
for both sexes.